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Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces

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  • Singh, Ajeet
  • Shukla, Anurag
  • Vijayakumar, V.
  • Udhayakumar, R.

Abstract

In this article, we discuss the asymptotic stability and mean square stability of stochastic differential equations of fractional-order 1<α≤2. We have considered the family of stochastic differential equations with variable delay in the state. For proving our main results, we apply the Banach fixed point theorem and imposed the Lipschitz condition on nonlinearity. Finally, we present an example to illustrate the obtained theory.

Suggested Citation

  • Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004495
    DOI: 10.1016/j.chaos.2021.111095
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    References listed on IDEAS

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    Cited by:

    1. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Shukla, Anurag & Vijayakumar, V. & Nisar, Kottakkaran Sooppy, 2022. "A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    3. Dossan Baigereyev & Dinara Omariyeva & Nurlan Temirbekov & Yerlan Yergaliyev & Kulzhamila Boranbek, 2022. "Numerical Method for a Filtration Model Involving a Nonlinear Partial Integro-Differential Equation," Mathematics, MDPI, vol. 10(8), pages 1-24, April.
    4. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    5. Yuhan Chen & Chenliang Li, 2022. "A Tensor Splitting AOR Iterative Method for Solving a Tensor Absolute Value Equation," Mathematics, MDPI, vol. 10(7), pages 1-9, March.
    6. Lichao Feng & Qiaona Wang & Chunyan Zhang & Dianxuan Gong, 2022. "Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
    7. Chendur Kumaran, R. & Venkatesh, T.G. & Swarup, K.S., 2022. "Stochastic delay differential equations: Analysis and simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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    9. Lu Zhang & Caishi Wang & Jinshu Chen, 2023. "Interacting Stochastic Schrödinger Equation," Mathematics, MDPI, vol. 11(6), pages 1-16, March.

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